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Commutators of
multiparameter flag singular integrals and applications
Xuan Thinh Duong, Ji Li, Yumeng Ou, Jill Pipher and Brett D. Wick |
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Vol. 12 (2019), No. 5, 1325–1355
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Abstract |
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We introduce the iterated commutator for the Riesz transforms in the multiparameter flag setting, and prove the upper bound of this commutator with respect to the symbol in the flag BMO space. Our methods require the techniques of semigroups, harmonic functions and multiparameter flag Littlewood–Paley analysis. We also introduce the big commutator in this multiparameter flag setting and prove the upper bound with symbol in the flag little bmo space by establishing the “exponential-logarithmic” bridge between this flag little bmo space and the Muckenhoupt weights with flag structure. As an application, we establish the div-curl lemmas with respect to the appropriate Hardy spaces in the multiparameter flag setting. |
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Keywords
multiparameter flag setting, flag commutator, Hardy space,
BMO space, div-curl lemma
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Mathematical Subject Classification 2010
Primary: 42B30, 42B20, 42B35
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Milestones
Received: 19 February 2018
Revised: 24 July 2018
Accepted: 16 September 2018
Published: 15 December 2018
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Authors |
| Xuan Thinh Duong | |
| Department of Mathematics Macquarie University Sydney Australia |
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| Ji Li | |
| Department of Mathematics Macquarie University Sydney Australia |
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| Yumeng Ou | |
| Department of Mathematics Baruch College The City University of New York New York, NY United States |
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| Jill Pipher | |
| Department of Mathematics Brown University Providence, RI United States |
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| Brett D. Wick | |
| Department of Mathematics Washington University–St. Louis St. Louis, MO United States |
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